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<div class="add">

<b>let </b><font color="Maroon">C</font> be   <a href="conlat_1.html#NM1">FormalContext</a>;<br/><b>let </b><font color="Maroon">O</font> be   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1" target="_self">Objects</a> of <font color="Maroon">C</font>;<br/>



<a NAME="E1:46"/><i><font color="Green">E29</font></i>: 
 <a href="conlat_1.html#G3" target="_self">ConceptStr</a>(# <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K2" target="_self">AttributeDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="conlat_1.html#K1" target="_self">ObjectDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">O</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K1" target="_self">ObjectDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">O</font></span>)</span> #) is   <a href="conlat_1.html#NM4">FormalConcept</a> of <font color="Maroon">C</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_1"><b>proof </b></a><div class="add">

<b>set </b><font color="Maroon">M'</font> =  <a href="conlat_1.html#G3" target="_self">ConceptStr</a>(# <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K2" target="_self">AttributeDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="conlat_1.html#K1" target="_self">ObjectDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">O</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K1" target="_self">ObjectDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">O</font></span>)</span> #);<br/>
<a NAME="E1:46_1"/>
<span class="p1">(<span class="default"><a href="conlat_1.html#K1" target="_self">ObjectDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> the <a href="conlat_1.html#U4" target="_self">Extent</a> of <a href="conlat_1.html#G3" target="_self">ConceptStr</a>(# <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K2" target="_self">AttributeDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="conlat_1.html#K1" target="_self">ObjectDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">O</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K1" target="_self">ObjectDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">O</font></span>)</span> #) <a href="hidden.html#R1">=</a> the <a href="conlat_1.html#U5" target="_self">Intent</a> of <a href="conlat_1.html#G3" target="_self">ConceptStr</a>(# <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K2" target="_self">AttributeDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="conlat_1.html#K1" target="_self">ObjectDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">O</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K1" target="_self">ObjectDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">O</font></span>)</span> #)
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E2:46_1"/>
 <a href="conlat_1.html#G3" target="_self">ConceptStr</a>(# <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K2" target="_self">AttributeDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="conlat_1.html#K1" target="_self">ObjectDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">O</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K1" target="_self">ObjectDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">O</font></span>)</span> #) is   <a href="conlat_1.html#NM4">FormalConcept</a> of <font color="Maroon">C</font>
 <b>by </b><i><a class="ref" href="conlat_1.html#D5" target="_self">Def5</a>, </i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:46"/>
for <font color="Olive">O'</font> being  <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1" target="_self">Objects</a> of <font color="Maroon">C</font><br/> for <font color="Olive">A'</font> being  <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2" target="_self">Attributes</a> of <font color="Maroon">C</font>  st  <a href="conlat_1.html#G3" target="_self">ConceptStr</a>(# <font color="Olive">O'</font>,<font color="Olive">A'</font> #) is   <a href="conlat_1.html#NM4">FormalConcept</a> of <font color="Maroon">C</font> &amp; <font color="Maroon">O</font> <a href="tarski.html#R1">c=</a> <font color="Olive">O'</font> holds <br/><span class="p1">(<span class="default"><a href="conlat_1.html#K2" target="_self">AttributeDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K1" target="_self">ObjectDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">O</font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Olive">O'</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">O'</font> be   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1" target="_self">Objects</a> of <font color="Maroon">C</font>;<br/><b>let </b><font color="Maroon">A'</font> be   <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2" target="_self">Attributes</a> of <font color="Maroon">C</font>;<br/>



<b>assume </b><a NAME="E1:46_2"/><i><font color="Green">E32</font></i>: 
(  <a href="conlat_1.html#G3" target="_self">ConceptStr</a>(# <font color="Maroon">O'</font>,<font color="Maroon">A'</font> #) is   <a href="conlat_1.html#NM4">FormalConcept</a> of <font color="Maroon">C</font> &amp; <font color="Maroon">O</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">O'</font> )
 ;<br/>

<b>then reconsider </b><font color="Maroon">M'</font> =  <a href="conlat_1.html#G3" target="_self">ConceptStr</a>(# <font color="Maroon">O'</font>,<font color="Maroon">A'</font> #) as   <a href="conlat_1.html#NM4">FormalConcept</a> of <font color="Maroon">C</font> ;<br/>
<i><font color="Green">E33</font></i>: <span class="p1">(<span class="default"><a href="conlat_1.html#K2" target="_self">AttributeDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">A'</font> = 
the <a href="conlat_1.html#U4" target="_self">Extent</a> of <font color="Maroon">M'</font>
<b>by </b><i><a class="ref" href="conlat_1.html#D5" target="_self">Def5</a></i>
<br/>.= 
<font color="Maroon">O'</font>

;<br/>
<i><font color="Green">E34</font></i>: <span class="p1">(<span class="default"><a href="conlat_1.html#K1" target="_self">ObjectDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">O'</font> = 
the <a href="conlat_1.html#U5" target="_self">Intent</a> of <font color="Maroon">M'</font>
<b>by </b><i><a class="ref" href="conlat_1.html#D5" target="_self">Def5</a></i>
<br/>.= 
<font color="Maroon">A'</font>

;<br/>
<a NAME="E5:46_2"/>
<span class="p1">(<span class="default"><a href="conlat_1.html#K1" target="_self">ObjectDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">O'</font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K1" target="_self">ObjectDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">O</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E6:46_2"/>
<span class="p1">(<span class="default"><a href="conlat_1.html#K2" target="_self">AttributeDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K1" target="_self">ObjectDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">O</font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">O'</font>
 <b>by </b><i>, , </i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:46"/>
(  <a href="conlat_1.html#G3" target="_self">ConceptStr</a>(# <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K2" target="_self">AttributeDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="conlat_1.html#K1" target="_self">ObjectDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">O</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K1" target="_self">ObjectDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">O</font></span>)</span> #) is   <a href="conlat_1.html#NM4">FormalConcept</a> of <font color="Maroon">C</font> &amp; ( for <font color="Olive">O'</font> being  <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U1" target="_self">Objects</a> of <font color="Maroon">C</font><br/> for <font color="Olive">A'</font> being  <a href="subset_1.html#NM2">Subset</a> of the <a href="conlat_1.html#U2" target="_self">Attributes</a> of <font color="Maroon">C</font>  st  <a href="conlat_1.html#G3" target="_self">ConceptStr</a>(# <font color="Olive">O'</font>,<font color="Olive">A'</font> #) is   <a href="conlat_1.html#NM4">FormalConcept</a> of <font color="Maroon">C</font> &amp; <font color="Maroon">O</font> <a href="tarski.html#R1">c=</a> <font color="Olive">O'</font> holds <br/><span class="p1">(<span class="default"><a href="conlat_1.html#K2" target="_self">AttributeDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K1" target="_self">ObjectDerivation</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">O</font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Olive">O'</font> ) )
 <b>by </b><i/>;<br/>


</div>
